PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.     

BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION

The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order impulsive differential equation.     

POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL SYSTEMS

In this paper, by utilizing a fixed point theorem on cone in Banach space, the author disscusses the periodic boundary value problem of second order differential systems. Some results on the existence of positive solutions are derived.     

SOLVABILITY OF M-POINT BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

1IntroductionRecentlytmultiplepointsboundaryvalueproblemsforordinarydifferentialequationsarcextensivelystudied,see[1-4].Inthispapertweconsiderthesolvabilityofthefollowingsecondorderordinarydifferentialequationwithm-pointboundaryvalueconditionswhere,fsatisfiesCaratheodory'sconditions,al,...,am--2havethesamesign,fi,...,(.--2E(0,1),eEL'(0,1),andthesignZdenotesthesumZ7=i'.InthecaseOfa=Zal/1,theproblem(1.1),(1.2)wasstudiedin[1],bymeansoftheLeray-Schaudercontinuationtheorem,whileinthecaseofor51a…     

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved.     

MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

This paper is concerned with the boundary value problem for a system of nonlinear third order differential equations. Under some suitable conditions, the existence and multiplicity of the positive solutions are established by using abstract fixed-point theorems.     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FIRST ORDER DELAY DIFFERENTIAL EQUATIONS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations.     

BOUNDARY VALUE PROBLEMS FOR SECOND ORDER MIXED-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS

We use the topological degree method to deal with the generalized Sturm-Liouville boundary value problem (BVP) for second order mixed-type functional differential equation x(t)=f(t,xt,xt), 0≤t≤T. Existence principle and theorem for solutions of the BVP are obtained.     

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.     

MULTIPLE POSITIVE SOLUTIONS OF NONRESONANT SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multiple positive solutions as well as C1[0, 1] multiple positive solutions is given by means of the fixed point theorems on cones.     

BOUNDARY VALUE PROBLEM FOR MIXED TYPE FUNCTIONAL DIFFERENTIAL SYSTEM

1 IntroductionIn the recent years, the existence problem of BVP of second order functionaldifferential equations of the forms[p(t)i(t)]' = f(t, xf, x(t)), (1)i(t) = f(t, x(t), x(al(t)),'', x(a.(t)), i(t)), (2)x(t) = f(t, x(t), x(al(t)),'', x(U.(t)), i(t), i(n(t)),'', i(fu(t))), (3)t -- r 5 al(t),D(t) 5 t, as 0 5 t 5 T,i = 1,2,'' Ink j = 1,2,'',m, subjectto some boundary value conditions have been considered by several authors(please see [1-4],[6] and the references therein). In these pa…     

非线性积分微分方程组奇摄动边值问题

本文讨论含积分算子的非线性微分方程组Ｒｏｂｉｎ边值问题的奇摄动,在适当假设条件下通过对角化技巧,利用逐步逼近法证明了解的存在,并得到直到Ｏ（ε＾Ｎ＋１）的按范数界限的一致有效估计。     

高阶拟线性椭圆型方程奇摄动问题

本文利用微分不等式和多重尺度，研究了一个高阶椭圆型偏微分方程摄动边值问题，并得到了一致有效的渐近展开式。     

二阶不连续微分方程周期边值问题解的存在性

本文研究Lienard方程x"+f(t,x,x')x'+g(t,x)=h(t,x,x')的周期边值问题,其中f,g,h均为Caratbeodory函数.利用Leray-Schauder度理论,在适当的条件下证明了该问题解的存在性.     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

二阶混合型泛函微分方程边值问题解的存在性

本文利用迭合度方法讨论二阶混合型泛函微分方程 x=f(t,x^t,x^t) 0≤t≤T的边值问题（BVP），得到这个边值问题解的存在性的一个充分条件。     

SUPERCONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEM

Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.     

TWO-POINT BOUNDARY VALUE PROBLEM FOR A CLASS OF SECOND-ORDER DIFFERENCE EQUATIONS

In this paper, we apply a critical point theorem and obtain the condition for the existence of three solutions to two-point boundary value problem of a second order nonlinear difference equation.     

泛函微分方程周期边值问题的正解

讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件.